Is there an easier way to create an inset extrude along a model?
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Blender actually has a tool that does exactly what you're looking for. It's called Inset, and can used by selecting the section you want to inset, and pressing I.

Basically what this tool does is create an extra edge around the perimeter of your selection then slide the new edge inwards (towards the selection). Thus, it has a few limitations to know. 

First, you will need an edge to select that is exactly where you want the split to be. It looks like you have this already. 

Second, since the new edge will slide along existing edges, the thickness of the new face loop (what you were using Bridge Edge Loops to make) will be limited by how long the connecting edges are. If you have a really dense mesh for example, the new edges can't slide very far before colliding with existing vertices. What I'm trying to say is that you want to make sure that you mesh has "room" for the "path" that you're trying to add. The Inset tool only adds faces, it won't remove them.

Proper topology will help a lot, but it should work regardless. You might just have to do a bit of trial and error to see what you need to tweak.